You cannot be insured under the public health insurance system.
Before coming to Germany, you need to show proof of health insurance that will cover your entire stay. Germany has strict regulations and may not accept certain travel/health insurance. There are some companies that are the cheapest but it will be rejected for visa applications.
Our partners Dr. Walter, a German insurance company offering over 50+ years worth of experience can supply coverage that will work for your visa application and stay in Germany. Contact us for more information.
If you move to Germany with private coverage then end up employed, you can cancel the Private Health Insurance and then switch to the public.